R Notebook

Epidemic timecourse from simulations vs data

National

Using the final parameter values from each chain

Fig. 1 Model calibration to incident cases (A) and incident deaths (B) reported by JHU CSSE for each state at 0.55% IFR assumptions, summed over entire country. (C) [Optional] Model comparison to hospitalizations (not fit). Shaded areas show 95% confidence intervals based on 4independent inference runs and black points/lines indicate data reported by JHU CSSE.

State-level

(for subset of states only now)

Fig. 2 Calibration of estimated incident cases and deaths to reported data from JHU CSSE, and validation of estimates for occupied hospital beds when compared to CDPH data. Here, modeled cases are calculated as a percent of modeled infection that is fit to county data. Black points represent actual data, lines represent means and shading represents the 95% prediction interval for each scenario at 0.55% IFR and 0.5% assumptions. Note that JHU CSSE data were reported as daily cumulative cases and deaths. In this figure, daily cumulative case counts were differenced in order to report the incident cases and deaths. In comparing the actual and modeled data, we emphasize that limited testing and reporting delays may affect the quality of the reported case data early on in the outbreak.

Likelihood trends

Likelihood by MCMC iteration: state-level

Fig. 3 GeoID-specific log-likelihood values by MCMC step. Here ‘chimeric’ values are the likelihood for accepted parameters in the chimeric likelihood, and ‘global’ values are the likelihood values for the proposed parameters of the chimeric likelihood, which are recorded in the global likelihood files. These two likelihood values are equivalent only at steps where the chimeric likelihood was accepted for that GeoID.**

Likelihood by MCMC iteration: national-level

Fig. 4 Total log-likelihood values by MCMC step (summed over all GeoIDs). Here ‘chimeric’ values are the total likelihood for accepted parameters in the chimeric likelihood, and ‘global’ values are the likelihood values for the proposed parameters of the chimeric likelihood, which are recorded in the global likelihood files. The chimeric (accepted) likelihood is always higher since acceptance decisions are made on a geoID-by-geoID level, and only accepted for GeoIDs where the acceptance would improve the geoID-specific likelihood. These two likelihood values would only be equivalent at steps where the chimeric likelihood was accepted for every single GeoID.**

Proportion of likelihoods accepted or rejected

Fig. 5 Acceptance rate of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate. Acceptance rate is averaged over all previous steps. **

Average acceptance as rolling mean over an interval

Fig. 6 Acceptance rate of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate. Acceptance rate is averaged over the previous10steps**

Cumulative acceptances

Fig. 7 Cumulative number of acceptances of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate**

Parameter inference trends

Basic SEIR parameter by MCMC iteration

Note: For these runs, these parameters are the same for all states and are fixed, not estimated, so nothing to plot

Fig. 8 SEIR parameters by MCMC step (‘chimeric’ values)**

Outcome model parameter values by MCMC iteration

Fig. 9 Inferred outcome parameter values by MCMC step for each GeoID.’Global’ values are the proposed parameters at each step, and ‘Chimeric’ values are the parameters accepted at the GeoID-level in the chimeric likelihood **

SNPIs by MCMC iteration

Fig. 10 Inferred paramter values by MCMC step for each GeoID.’Global’ values are the proposed parameters at each step, and ‘Chimeric’ values are the parameters accepted at the GeoID-level in the chimeric likelihood **

HNPIs by MCMC iteration

This section might be blank if no outcome parameters were fit

Fig. 11 Inferred paramter values by MCMC step for each GeoID.’Global’ values are the proposed parameters at each step, and ‘Chimeric’ values are the parameters accepted at the GeoID-level in the chimeric likelihood **

Seeding parameters

Don’t have any plots developed yet for seeding values

Correlations between fit parameter values (identifiability analysis)

Correlations are for within a particular MCMC chain, treating each iteration as a sample

For each state individually

## [1] "California"

## [1] "Florida"

## [1] "Illinois"

## [1] "NewYork"

## [1] "Ohio"

## [1] "Texas"

## [1] "Washington"

Average over all states

Variance of posterior vs proposal step size

This is a way of measuring whether adaptive MCMC could help. (Ignore covariance for now). If observed std >> perturb_sd, suggests that proposal too small. If observed_sd << perturb_sd, suggests proposal too big. Done for each parameteres

Final global likelihood values

#OTHER

Example code to read in SEIR values directly